Billionaire investor Carl Icahn may be biting off more of the Apple than he can chew.

The wily septuagenarian on Thursday said he would consider a proxy battle for board seats at Apple if the board ignores his request to pump up its stock buyback program to $150 billion over three years from $60 billion.

“If I felt that I could win one or two seats on the board, I would certainly do it,” Icahn told CNBC on Thursday after he released a letter he wrote to CEO Tim Cook about the buyback.

Icahn, in the letter, said if Apple undertook the mega-buyback immediately, its share price could spike to about $1,260.

Apple closed Thursday at $531.91, up 1.3 percent.

But Icahn, who successfully agitated for change recently at Dell, Dynegy and Chesapeake Energy, may be picking on too large and too successful a target with Apple, many critics said Thursday.

Apple, the most valuable US company, with a market cap of $483 billion, has seen its shares spike 450 percent over the last five years.

Granted, Apple shares are down nearly 13 percent over the last 12 months, but institutional shareholders appear content with Cook’s management.

“Even though Icahn can play in the deep end of the pool, Apple … that’s just a huge target,” one institutional investor in Apple told The Post.

“I think it’s a little bit of an uphill battle,” he said.

Hedge-fund manager David Einhorn learned the hard way how loyal Apple shareholders can be after he urged them to tilt at a much smaller windmill — to reject a proposal at February’s shareholder meeting.

In a rare move, a slew of institutional shareholders came out ahead of the vote to say they were siding with Apple.

Still, shareholders also say that Icahn’s push for Apple to do something with its massive $150 billion cash hoard is “resonating.”

“It can’t continue. It’s unsustainable in my mind. They need to either make some acquisitions or give some of it back to investors,” an investor told The Post.

Bond investor Bill Gross was less sympathetic to Icahn’s request.

After the letter came out, Gross blasted Icahn on Twitter, telling him to “leave #Apple alone & spend more time like Bill Gates.”

“If #Icahn’s so smart, use it to help people not yourself,” Gross whined.

In his letter to Cook, Icahn said he boosted his stake in Apple by 22 percent to 4.7 million shares from 3.8 million at the end of September when he met the CEO for dinner.

At the meal, Cook said he expected to get back to Icahn about his buyback plan in about three weeks, Icahn said.

Apple, through a spokesman, declined to comment on the Icahn letter.

However, the activist could learn what Cook and the board decided as soon as Monday, when Apple is slated to report quarterly results.